What is the directrix (x-4)^2=4(y+2) ?

The directrix (x-4)^2=4(y+2) is y=-3

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directrix (x-4)^2=4(y+2)

directrix

(x - 4)^{2} = 4 (y + 2)

y = - 3

Solution steps

Rewrite

(x - 4)^{2} = 4 (y + 2)

in the standard form:

4 \cdot 1 \cdot (y - (- 2)) = (x - 4)^{2}

(h, k) = (4, - 2), p = 1

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(4, - 2)

y-coordinate

y = - 2 - p

y = - 2 - 1

Refine

y = - 3

16 x^{2} - 25

- x^{2} + 64 x - 292

y = 5 x^{2} + 13 x - 6

y = 3 x^{2} + 6 x - 12

(x - 5)^{2} = 20 (y - 5)